A mathematical model for fixed-end moments of a beam subjected to a uniformly distributed load taking into account the shear deformations

This paper presents a mathematical model for beams subjected to a uniformly distributed load considering the shear deformations to obtain fixed-end moments. The consistent deformation method is used to solve such problems; a method based on the superposition of effects and by means of the Bernoulli-Euler theory is obtained the deformations at any point of the beam. Traditional methods used for beams subjected to a uniformly distributed load did not consider the shear deformations. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements, fixed-end moments are calculated at any cross section of the beam using the respective integral representations as mathematical formulas. © 2013 ICIC International.